# Find the shortest distance from the point P = (2,2,5)

2,712

Hint: Let $u=\langle 2,2,5\rangle$ and $v=\langle 6,5,4\rangle$, and find $\displaystyle d=\frac{|u\times v|}{|v|}$.

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### Yusha

Updated on August 15, 2022

• Yusha 9 months

Find the shortest distance from the point $P = (2,2,5)$ to a point on the line given by $l:(x,y,z) = (-6t, -5t, -4t)$

So I've got the matrix that I think it should look like which is

$\begin{bmatrix}-6&-5&-4\\2&2&5\end{bmatrix}$ but what exactly am I solving here

• Yusha almost 7 years
The derivative of $d(t) = 0$
• Kaj Hansen almost 7 years
I'm recommending minimizing $f(t) = (d(t))^2$ by first finding $\displaystyle \frac{df}{dt}$.
• Yusha almost 7 years
there is no $f$
• Kaj Hansen almost 7 years
I'm just defining it to be the function $(d(t))^2$ for notational convenience.
• Yusha almost 7 years
This is not a calculus class, this is linear algebra. Shouldn't have to use any sort of calculus for this
• Kaj Hansen almost 7 years
That's alright; you don't have to accept my answer, and we can wait on someone else. I believe in having diverse solutions posted nevertheless.